We introduce a new graph problem, the token dropping game, and we show how to solve it efficiently in a distributed setting. We use the token dropping game as a tool to design an efficient distributed algorithm for stable orientations and more generally for locally optimal semi-matchings. The prior work by Czygrinow et al. (DISC 2012) finds a stable orientation in O(Δ5) rounds in graphs of maximum degree Δ, while we improve it to O(Δ4) and also prove a lower bound of Ω(Δ).
@article{arxiv.2005.07761,
title = {Efficient Load-Balancing through Distributed Token Dropping},
author = {Sebastian Brandt and Barbara Keller and Joel Rybicki and Jukka Suomela and Jara Uitto},
journal= {arXiv preprint arXiv:2005.07761},
year = {2021}
}